A series solution of the Cauchy problem for the generalized d-dimensional Schrödinger equation with a power-law nonlinearity

Authors:
A. Shidfar;A. Molabahrami;A. Babaei;A. Yazdanian
Affiliations:
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran;Department of Mathematics, Iran University of Science and Technology, Tehran, Iran and Department of Mathematics, Ilam University, PO Box 69315516, Ilam, Iran;Department of Mathematics, Iran University of Science and Technology, Tehran, Iran;Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, the Cauchy problem for generalized d-dimensional Schrodinger equation with a power-law nonlinearity is studied. Three methods, homotopy analysis method (HAM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM), are applied to obtain series pattern solutions of the mentioned Cauchy problem. The recurrent relations, for solving the mentioned Cauchy problem, is introduced. For some cases of given initial conditions, we obtain the closed form of the exact solutions.